Blaise Pascal: intsomi yevili le-roulette
Isazi sezibalo esidla ngokunikwa udumo lokuyila ivili, ebezama ukwakha enye into.
UPascal (1623–1662) wenza uvavanyo ngezixhobo zentshukumo engapheliyo ngeminyaka yee-1650. Ivili elijikelezayo eliphantse lingabinakuxhuzula ekuthiwa lelakhe linokuba ngukhokho we-irotha ye-roulette; esi sigqibo singokwesithethe kunokuba sibhalwe phantsi.
Isazi sezibalo
UBlaise Pascal wakha isixhobo sokubala soomatshini eneminyaka elishumi elinesithoba, wangqina iziphumo kwijiyometri ye-projective esekwishumi elivisayo, wenza umsebenzi osisiseko ngoxinzelelo nangokungabikho komoya, kwaye ngo-1654, ngeeleta noPierre de Fermat, wasombulula “ingxaki yamanqaku”: indlela yokwahlula ngokufanelekileyo iibheji zomdlalo wethamsanqa ophazamisekileyo. Impendulo yabo, yokwahlula ngokwe-mathubaizibaloAmathubaIthuba lesiphumo, ukusuka ku-0 ukuya ku-1 okanye ku-0% ukuya ku-100%. Inani elinye: 1/37 = 2.70%.Funda yonke → omdlali ngamnye okuphumelela ukuba umdlalo ubuqhubekile, yimvelaphi yexabiso elilindelekileyoizibaloIxabiso elilindelekileyoIsiphumo esiphakathi kwibheji nganye ekuhambeni kwexesha elide. −1/37 yebheji kuyo yonke ibheji eqhelekileyo yaseYurophu.Funda yonke →. Lonke ubalo lwe-EV kule sayithi luvela kwezo leta.
Ingaba wayekho umatshini we-roulette kaBlaise Pascal?
Phakathi kweminyaka yee-1650 uPascal wasebenza kumatshini wentshukumo engapheliyo kwaye kuthiwa wakha ivili elilinganiswe kakuhle elajikeleza ixesha elide ngokuxhuzula okuncinci. Ibali lokuba eli vili laba yi-irothaizixhoboIrothaInxalenye ejikelezayo yevili ethwele izikhewu.Funda yonke → ye-roulette liphindwa kwiimbali ezininzi kwaye alibhalwanga nakweyiphi imithombo yokuqala. Kunokwenzeka ukuba abaqhubi bamaziko eedolophu zemithombo ngenkulungwane ye-18 basebenzisa igama lakhe ukuthengisa. Ayiyonto iLebhu inokuyamkela ngobungqina obukhoyo.
Amathuba, ngamazwi akhe nangawethu
Iileta zango-1654 azikhankanyi i-roulette, eyayingekabikho. Zibuza: abadlali ababini bafuna amanqaku amathathu ukuze baphumelele imbiza; bayeka ku-2–1; imbiza kufuneka yahlulwe njani? Impendulo kaPascal isebenzisa into esinokuyibiza ngoku ngokuba lulindelo olunemeko kunye nengxoxo ephindaphindayo esihla ngomthi wokuqhubeka okunokwenzeka. UHuygens wayifunda imbalelwano kwaye ngo-1657 wapapasha incwadi yokuqala yokufunda ngolindelo. Igama elithi “ulindelo” lelakhe.
UPascal noFermat basombulula ingxaki yamanqaku: ixabiso elilindelekileyo njengexabiso elifanelekileyo lemeko.
UHuygens, De Ratiociniis in Ludo Aleae: incwadi yokuqala eshicilelweyo ngolindelo.
UJakob Bernoulli, Ars Conjectandi: umthetho wamanani amakhulu.
I-roulette ichazwa eParis. Yonke intlawulo ingu-36/n − 1: EV = −1/37 (okanye −2/38).
Uvavanyo lwe-chi-square lukaPearson, lubonisiwe kwimijikelo ye-roulette.
Konke oku kungentla, kule sayithi, kwibhrawuza.
Ibheji kaPascal
Eyona ngxoxo idumileyo kaPascal ngokubheja ayimalunga ne-roulette kodwa ngoThixo: “ibheji” ekwi-Pensées ebeka ukholo njengebheji enomvuzo ongapheliyo. Yingxoxo yexabiso elilindelekileyo, kwaye kokokuqala umntu esebenzisa ithiyori yezigqibo ukuxhasa nantoni na. Abadlali be-roulette ababiza uPascal ngenxa yevili babiza uPascal ongenguye; lowo ubalulekileyo ngulowo wabonisa indlela yokubeka ixabiso kwingcakazo.
Into ehlekisayo
Nokuba uPascal walakha okanye akalakhanga ivili lokuqala le-roulette, umdlalo ungumzekelo ococekileyo womsebenzi wakhe wokwenyani: isixhobo esivela kwindoda eyangqina ukuba awunakufumana into ngento engekhoyo (intshukumo engapheliyo iyasilela; ulindelo luyagcinwa), esetyenziswa ukubonisa kwanto leyo kwizigidi ezimbalwa zabadlali ngonyaka.
Imibuzo
Wayehamba kwizangqa zokungcakaza eParis ekuqaleni kweminyaka yee-1650, kwaye yiyo loo nto ingxaki yamanqaku yafika kuye ngoChevalier de Méré. Akukho rekhodi yokuba wayedlala ngemali ngokunzulu.
Kuba libali elihle kwaye kuba abakhuthazi beekhasino benkulungwane ye-19 babelithanda. Liphinde nombhalo osemazantsi.
Uncumo
Wangqina ukuba awunakufumana into ngento engekhoyo. Emva koko umntu othile wakha ikhasino phezu koko.
Imithombo
- Pascal, B. & Fermat, P. Correspondence on the problem of points.
- Huygens, C. De Ratiociniis in Ludo Aleae.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.